In the past, for example, there is a lamp including a GX53-type cap as a flat-type lamp used in a luminaire such as a downlight arranged to be embedded in a setting surface of the ceiling or the like. The lamp includes a light-emitting module substrate including LEDs, which are semiconductor light-emitting devices, as light sources, a housing configured to house the light-emitting module substrate and having translucency in a lower part opposed to the light-emitting module substrate, a GX53-type cap including a pair of lamp pins provided on the upper side of the housing, and a thermal radiation sheet arranged in the cap. In the lamp, after the cap is pressed against a socket attached to a luminaire main body of a luminaire, the lamp is attached to the socket by being rotated a predetermined angle. In this attached state, the cap is electrically connected to a power supply side. The thermal radiation sheet is brought into contact with a thermal radiator of the luminaire main body and thermally connected thereto. Consequently, it is possible to radiate heat generated in the LEDs.